Class: HeadMusic::Rudiment::Tuning::Meantone

Inherits:
HeadMusic::Rudiment::Tuning show all
Defined in:
lib/head_music/rudiment/tuning/meantone.rb

Overview

Quarter-comma meantone temperament Optimizes major thirds to be pure (5:4) at the expense of perfect fifths

Constant Summary collapse

INTERVAL_RATIOS =

Frequency ratios for intervals in quarter-comma meantone temperament The defining characteristic is that major thirds are pure (5:4) and the syntonic comma is distributed equally among the four fifths

{
  unison: Rational(1, 1),
  minor_second: 5.0**(1.0 / 4) / 2.0**(1.0 / 2),     # ~1.0697
  major_second: 5.0**(1.0 / 4),                       # ~1.1892 (fourth root of 5)
  minor_third: 5.0**(1.0 / 2) / 2.0**(1.0 / 2),      # ~1.5811
  major_third: Rational(5, 4),                        # Pure major third (1.25)
  perfect_fourth: 2.0**(1.0 / 2) / 5.0**(1.0 / 4),   # ~1.3375
  tritone: 5.0**(3.0 / 4) / 2.0**(1.0 / 2),          # ~1.6719
  perfect_fifth: Rational(3, 2),                      # ~1.4953 (slightly flat)
  minor_sixth: 2.0**(3.0 / 2) / 5.0**(1.0 / 4),      # ~1.6818
  major_sixth: 5.0**(3.0 / 4),                        # ~1.8877
  minor_seventh: 2.0**(3.0 / 2) / 5.0**(1.0 / 2),    # ~1.8877
  major_seventh: Rational(25, 16),                    # ~1.5625
  octave: Rational(2, 1)                              # Octave (2.0)
}.freeze

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(reference_pitch: :a440, tonal_center: nil) ⇒ Meantone

Returns a new instance of Meantone.



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# File 'lib/head_music/rudiment/tuning/meantone.rb', line 28

def initialize(reference_pitch: :a440, tonal_center: nil)
  super
  @tonal_center = HeadMusic::Rudiment::Pitch.get(tonal_center || "C4")
end

Instance Attribute Details

#tonal_center ⇒ Object (readonly)

Returns the value of attribute tonal_center.



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# File 'lib/head_music/rudiment/tuning/meantone.rb', line 26

def tonal_center
  @tonal_center
end

Instance Method Details

#calculate_tonal_center_frequency ⇒ Object (private) 



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# File 'lib/head_music/rudiment/tuning/meantone.rb', line 51

def calculate_tonal_center_frequency
  # Use equal temperament to get the tonal center frequency from the reference pitch
  interval_to_tonal_center = (tonal_center - reference_pitch.pitch).semitones
  reference_pitch_frequency * (2**(interval_to_tonal_center / 12.0))
end

#frequency_for(pitch) ⇒ Object 



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# File 'lib/head_music/rudiment/tuning/meantone.rb', line 33

def frequency_for(pitch)
  pitch = HeadMusic::Rudiment::Pitch.get(pitch)

  # Calculate the frequency of the tonal center using equal temperament from reference pitch
  tonal_center_frequency = calculate_tonal_center_frequency

  # Calculate the interval from the tonal center to the requested pitch
  interval_from_tonal_center = (pitch - tonal_center).semitones

  # Get the meantone ratio for this interval
  ratio = ratio_for_interval(interval_from_tonal_center)

  # Calculate the frequency
  tonal_center_frequency * ratio
end

#ratio_for_interval(semitones) ⇒ Object (private) 



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# File 'lib/head_music/rudiment/tuning/meantone.rb', line 57

def ratio_for_interval(semitones)
  # Handle octaves
  octaves = semitones / 12
  interval_within_octave = semitones % 12

  # Make sure we handle negative intervals
  if interval_within_octave < 0
    interval_within_octave += 12
    octaves -= 1
  end

  # Get the base ratio
  base_ratio = case interval_within_octave
  when 0 then INTERVAL_RATIOS[:unison]
  when 1 then INTERVAL_RATIOS[:minor_second]
  when 2 then INTERVAL_RATIOS[:major_second]
  when 3 then INTERVAL_RATIOS[:minor_third]
  when 4 then INTERVAL_RATIOS[:major_third]
  when 5 then INTERVAL_RATIOS[:perfect_fourth]
  when 6 then INTERVAL_RATIOS[:tritone]
  when 7 then INTERVAL_RATIOS[:perfect_fifth]
  when 8 then INTERVAL_RATIOS[:minor_sixth]
  when 9 then INTERVAL_RATIOS[:major_sixth]
  when 10 then INTERVAL_RATIOS[:minor_seventh]
  when 11 then INTERVAL_RATIOS[:major_seventh]
  end

  # Apply octave adjustments
  base_ratio * (2**octaves)
end